Do you know exactly why the accountant wants this? I can’t imagine for accounting what would be the purpose for a unique ID for a work period, since your accountant would most likely not care about work periods and more so about daily / weekly / monthly sales. Might be a good start to just ask exactly what the accountant needs this for because you may find the reason is easier to solve and they really don’t need the unique ID.
Failing that, I believe each work period does have a unique ID stored in the database, however the only way to get that to show on a report would be to use the Custom Reports feature, which is only available in either V4 with the paid Custom Reports module add on, or V5.
The re-open settled ticket feature (which is also needed for the associated refund features) was added in V4.1.38 (according to screenshots) - you need the “More Ticket Actions” module installed to do it which is only available in V4. I believe you are referring to this tutorial which is for V4 and above only:
In V3, the only refund feature I have used is a simple refund via the Cash account. It isn’t linked to any ticket and just lets you refund directly from your cash account. It was a long time ago I dealt with that but I believe it was quite easy to setup.
I also found on the forum this tutorial, some asked about V3 and Emre said it should work but not tested. From my V3 experience in the past it looks likely it will work. But again you lost any link to the original ticket where the refund is from.
If you want paid support, this is something I can do, my company provides professional services for SambaPOS and we have worked with V3 in the past and still support some clients using it. However I would suggest you look over those comments I made above first because really I would recommend you upgrade to V5 or at least V4 as that should resolve most of your issues.
If you want paid support you can send me a PM.